Maximum performance take-off director



Aug. 9, 1966 c. A. NEUENDORF ETAL 3,265,334

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HAXIMUH PERFORMANCE TAKE-OFF DIRECTOR 1e Sheets-Shet 1e Original FnegiJune 25', 1962 United States Patent 0 Road, Burlington, Mass. Originalapplication June 25, 1962, Ser. No. 205,135,

now Patent No. 3,200,642, dated Aug. 17, 1965. Divided and thisapplication Feb. 24,1965, Ser. No.

1 Claim. (Cl. 244-77) The invention described herein may be manufacturedand used by or for the United States Government for governmentalpurposes Without payment to us of any royalty thereon.

This is a division of application Serial No. 205,135, filed June 25,1962.

The purpose of this invention is to provide a director which will enablea pilot to obtain maximum take-off performance without visual referenceto the ground.

Investigations leading to the design of the director established thatmaximum performance results when the take-off is accomplished in twophases, in the first of which a constant angle of attack is maintainedand in the second of which a constant velocity is maintained, and inwhich the transition from the first phase to the second phase occurswhen the acceleration of the aircraft has fallen to zero. Briefly, thedirector described herein is a device to enable the pilot to control theaircraft in such K manner as to take off in accordance with theabovest-ated program.

Accurate take otf instrumentation is especially important in the case oflarge heavily-loaded aircraft. In such aircraft, establishing thecorrect attitude for lift-off is of primary concern. For example, in theKC'135, a lift-off attitude error of only two degrees can either extendthe ground roll by 3200 feet or result in take-off flight perilouslyclose to stall conditions, depending upon the direction of the error.This situation makes the use of an attitude gyro, the instrument usuallyemployed to supply pitch information during take-off, undesirable sincethe indication of this instrument is affected by the acceleration of theaircraft during ground roll, with the result that an erroneousindication of the liftoff attitude may be given. In order to avoid thissource of error, the director described herein obtains pitch informationfrom an angle-of-attack sensor which is unaffected by acceleration, thepitch angle and the angle of attack being equal during ground-roll.

The invention will be described in more detail with reference to theaccompanying drawings in which:

FIG. 1 illustrates the flight path angles of an aircraft,

FIG. 2 shows the forces and moments acting on an aircraft,

FIG. 3 shows the excess thrust available at various airspeeds for atypical cargo aircraft,

FIG. 4 shows time plots of V, V, a and 'y for a constant pitch angletagke-olf,

FIG. 5 shows altitude vs. distance at reduced thrust for a constantpitch angle take-off,

FIG. 6 shows altitude vs. distance for take-offs at constant pitchangles of various values,

FIG. 7 shows the effects of various lift-off speeds in constant pitchangle take-offs,

FIG. 8 shows time plots of V, V, h and 'y for a typical take-off withconstant angle of attack,

FIG. 9 gives plots of altitude vs. distance for take-offs at variousconstant angles of attack,

3,265,334 Patented August 9, 1.966

FIG. 10 shows the effects of various lift-off speeds using a constantangle of attack,

FIGS. 11a and 11b show take-off flight paths for'various variables in atypical aircrafts equations of :motion,

FIG. 12 shows altitude vs. distance for constant velocity take-offsunder various thrust conditions,

FIG. 13 shows time plots of V, V, 'y and at for a takeoff at constantvelocity,

FIGS. '14 and 15 show the take-off performance of a typical aircraftcontrolled by a flight director in accordance with the invention,

FIG. 16 is a logical diagram of a flight director in accordance with theinvention,

FIG. 17 shows a practical embodiment of the system shown in FIG. 16, and

FIG. 18 shows a suitable rectifier for use in FIG. 17.

The following symbols are used in the specification:

FLIGHT MECHANICS To better follow the various stages leading to thedevelopment of the takeoff indicator described herein, a

review of flight mechanics and the take-off problem is desirable,together with an analysis of the vertical gyro and the angle-of-attac'kindicator presently used as pitch control indicators.

Flight dynamics FIG. 1 shows the flight angles of an aircraft and FIG. 2the forces and. moments acting on an aircraft. In developing the forceequations the wind axis reference system is used. In this system, thereference axis is always aligned with the velocity vector of theaircraft, as shown in FIG. 1, where 0, the pitch angle, is defined asthe angle between the horizon and the wing chord. As shown, the angle 7is the flight path angle measured from the horizon to the wind axis; andthe angle of attack a is the angle between the wind axis and the wingchord.

If all forces acting on the aircraft are assumed to act through theaircraft center of gravity, their force vectors will be as shown in FIG.2. The velocity vector V, shown as a reference, is tangent to the flightpath and coincident with the wind axis, and is in the direction offlight of the aircraft; drag D is in the opposite direction. The lift Lis perpendicular to the wind axis and the weight W is acting along thetrue vertical. In this particular diagram, the thrust vector T isassumed to act along the wing chord of the aircraft. The moment actsabout the center of gravity.

By summing the forces with reference to the wind axis gravity, thefollowing equations are derived:

where M is a complex function primarily of V, and 6 (elevator deflectionangle).

From FIG. 2, it can be seen that: +v

The moment Equation 3 can be neglected when'only the maximum aircraftresponse is considered, because the inertia term only tends to delay anyrotational response. In this preliminary analysis, rotational responsetime is not a factor. Evaluation is based only on relative responsemagnitudes and, therefore, the moment equation is neglected. With theremaining equations, it is then possible to represent an aircraftsmaximum response characteristics.

Under flight conditions where the drag forces (including W components)are less than the thrust forces, the aircraft will have excess thrust.From Equations 1 and 2, it can be shown that this thrust can be used toproduce acceleration either entirely along the flight path, entirelyperpendicular to the flight path, or in various combinations betweenthese two extremes. FIG. 3(a) shows the excess thrust available atvarious airspeeds for a typical cargo aircraft. This excess thrust canthen be used to generate the acceleration (V) values, as shown in FIG.3(b), or to generate the rate of change of flight path values shown inFIG. 3(a). Any compromise, therefore, would be between these maximumvalues. Since utilization of these two parameters is of prime importanceduring the initial climb phase, further discussion of these parameterswill be continued later.

TAKE-OFF ANALYSIS A complete take-off can be divided into three distinctphases: (1) ground-roll; (2) transition; and (3) initial climb.

The ground-roll phase begins when the aircraft starts the take-off rolland ends when rotation speed is obtained. The transition phase beginswhen the aircraft has suflicient rotation speed and ends when theaircraft leaves the ground (lift-off). Initial-climb begins afterlift-off and continues until flaps are up.

By rotation it is meant that the aircraft physically rotates about itspitch axis, that is, the nose raises and, as shown in FIG. 1, the angles0 and a are generated. At this time, the aircraft leaves its three-pointattitude and assumes an attitude necessary to break ground" at theproper lift-ofl speed. Normally, the lift-off speed (V is 1.2 times thestalling speed of the aircraft (V Although take-oif is possible atspeeds nearer to V restrictions such as safety of flight prohibits theuse of these speeds. Disturbances, such as gusts or excessive use ofcontrols by the pilot, may cause the airspeed to fall beloW the stallingspeed and level flight will not be maintained. Also, a speed greaterthan V must be maintained in order to curve the flight path as requiredduring the climb-out phase. Another restriction is the physicalconstruction of the aircraft. In the case of the KC-135, the refuelingboom will strike the runway at a take-off attitude greater than 12,which corresponds closely to l.2V Air speeds in excess of 1.2V are, ofcourse, allowable but will result in an extended ground roll. For aheavilyloaded aircraft, this ground-roll distance is critical.

Ground-roll phase The purpose of this phase is to accelerate theaircraft to the lift-off velocity as soon as possible, thus reducing theground-roll distance. During this phase, only lateral control isnecessary and since only longitudinal effects during take-off areanalyzed, the ground-roll phase will not be considered.

Transition phase As the airspeed approaches V the aircraft is rotated tothe desired lift-off attitude. This attitude depends upon the aircraftand the take-off conditions, but normally an attitude is establishedwhich would result in a lift-off velocity of approximately 1.2V Asrotation begins, the angle on is increased. Since the aircraft is stillon the runway, the flight path angle 7 is zero and 0c is equal to 0. Asa and airspeed increase, the lift and drag also increase. The increaseof the drag force, due to an increase of a and airspeed, only tends toreduce the excess thrust which reduces V. As soon as the lift forcesbecome greater than the gravitational forces, the aircraft will leavethe runway and a 'y will result. At this time, the transition phase endsand the initial climb phase begins.

Initial climb phase In this phase, the utilization of the excess thrustis of prime importance. As mentioned, this thrust could be used toobtain all 'y', all V, or a compromise between the two. Neither extremeis desirable because an increase of On a typical take-off, the aircraftis accelerated 0n the runway to the normal rotation speed. As the speedof the aircraft approaches V during the ground roll, the pilot startsrotating the aircraft to the desired lift-01f attitude. As the angle ofattack increases, the lift of the aircraft also increases; untilfinally, as the break-ground speed is attained and the lift-off attitudeis established, the lift component of force becomes greater than thegravitational forces and the aircraft leaves the runway. At lift-off,the angle of attack and the angle 6 are equal and 'y is zero. The excessthrust is now used to obtain acceleration of both V and 5 Since both Vand 'y are increasing while the pilot maintains a constant (9, the angleon decreases. The angle 6 is maintained constant until V 20 knots isobtained. At this time, the excess thrust is no longer needed toaccelerate along the flight path, and V is made zero. All the excessthrust is then used to obtain acceleration of '9.

The typical initial climb phase, as just explained, appears to be acombination of constant 0 and constant V. This, in effect, is true.However, the use of this type climb is not based on obtaining themaximum performance for which the aircraft is capable, but rather themaximum performance obtainable with present instrumentation. As will beexplained later, take-off performance can be improved with differentinstrumentation. Since the pilot has only the attitude gyro and, in somecases, an angle-of-attack indicator, the take-off characteristicsobtained by using each of these indicators independently are of interestand will be analyzed next.

Present pitch control indicators In this analysis, the vertical gyro andthe angle-ofattack indicators were flown on an analog computer throughthe initial climb phase to determine the advantages and disadvantages ofeach. This analysis will use the specifications of the KC-135. Inpreparing for the computer analysis, Equations 1, 3 and 4 were used.specifications and initial conditions were:

(1) V =276 f.p.s.

(2L0: 12:0LO 'YLO:0 (4) W=297,000 lbs. (5) T =53,00O lbs. (6) Flaps setat 30 (7) Gear down Parameter time plots and aircraftaltitude-versus-distance plots were recorded. The time plots show thecomplete parameter reaction for each indicator. Thealtitude-versusdistance plots show the distance need to gain 500 feet ofaltitude. The distance plots also show the flight path obtained with theassumed loss of one engine at various times in the flight.

Constant 0 take-ofi The attitude gyro, which is installed in mostaircraft, is a gyroscopic instrument which should give sensitive,reliable information. However, the instrument has several disadvantages,one being that it is sensitive to acceleration forces. Because of theacceleration present during the ground-roll phase, the attitude gyro canprecess as much as 7. Even the improved attitude gyros precess as muchas 2, which is still too great an error if maximum performance is to beobtained. Besides these objections, the instrument is difficult to readaccurately, as small incremental changes are not discernible, and theactual magnitude of 0 can only be approximated. However, neglectingthese faults, an analog computer analysis and discussion of a constant 0take-off follow. The conditions and techniques of analysis are as statedearlier.

In this type of take-off, the aircraft rotates to some selected pitchangle at V and maintains this angle constant from lift-off untilcompletion of the initial climb. Just after rotation, the aircraft willhave an angle on equal to 0 and the flight path angle will be zero. Atthis time,

the excess thrust produces a positive V and V increases. This increasein velocity produces additional lift. This excess will generate someflight path acceleration and, therefore, some 'y. Since 0 is heldconstant and 'y is increasing, the angle a must decrease. Although 0:does decrease, the resultant lift continues to increase because V 'hasincreased. This trade-off of V and a continues until the excess thrustis balanced by the drag and weight components, and until '9 and V arezero.

The effects of the constant 0 initial climb are clearly shown on thetime plots of FIG. 4. It can be seen that, at lift-off, 'y is zero; a is12; V is 276 f.p.s.; and V is 2 f.p.s. The flight path angle increasesimmediately after lift-off, as shown by an increasing 7. Although Vincreases, the value of V is diminishing. As equilibrium is reached, Vgoes to zero; 7 remains constant at 4; cc remains constant at 8; and Vremains constant at 325 fps. The altitude vs. distance plots of thisphase are shown in FIG. 5 for normal and reduced thrust. FIG. 6 showsthe effect of various climb angles, and FIG. 7 shows the effect ofrotating the aircraft at various lift-off airspeeds.

The

Constant a take-ofi Although not in widespread use as an attitudecontrol indicator, the angle-of-attack indicator is a means ofcontrolling the pitch of an :aircarft. As an instrument, anangle-of-attack indicator has several advantages over the attitude gyro.The instrument is not acceleration sensitive; therefore, no errors areincurred because of groundroll acceleration. In addition, the indicatorcan read directly the magnitude of u and the instrument has asatisfactory accuracy of 0.1. However, one problem does exist: Becausethe sensor only measures local angle of attack, a position must be foundwhere the relation between local and remote angle of attack is constant,or, in other words, the sensor must be mounted on the aircraft at alocation where the wind direction at the sensor with respect to thechord of the aircraft win-g, which direction is influenced by the airflow over the aircraft surfaces, has a constant relation to the truewind direction with respect to the chord, over the usable range of theangle of attack. However, this is possible Within the limits ofinstrument accuracy. Therefore, under the assumption that the use of ana indicator is entirely feasible, the explanation of the constant orinitial climb phase follows.

In this take-off, the aircraft rotates to a selected angle of attack atV and maintains this on throughout the initial climb. As in the constant0 take-01f, the excess thrust is producing a positive V at lift-off.Since a is held constant, and at V the lift is equal to weight, anyincrease in V will cause the lift to become greater than the weight,resulting in a positive '1. The increase in 7 further reduces the excessthrust available which, in turn, reduces V. Eventually, due to theincreasing 'y, the excess thrust producing V is exhausted. However, a.positive & is still generated. This is seen as point 1 in FIG. 8 on thecomputer time plots. The increase in 7 after V has gone to zero resultsin an increase in drag components, which further decreases velocity.This decrease in V reduces the lift which, in turn, decreases At point 2on FIG. 8, the V and, consequently, the lift have been reduced to suchan extent as to cause 5 to become zero. Since 7 is still at its peak,the velocity continues to decrease and a becomes negative and 7decreases. V, although negative, is building up until at point 3 of FIG.8 it becomes positive. As V starts to increase, the lift in creaseswhich results in 5 increasing until at point 4, '9 equals zero, V ismaximum, and the cycle repeats, thus generating the phugoid path. It canbe seen also that the condition which generates this phugoid is thephase relation between y and V. It is noted in FIG. 9 that the phugoidis steeper when on is increased, and it is further aggravated when thevelocity is increased as shown in FIG. 10. Certainly, any take-off underthese conditions is completely unsatisfactory. However, by comparing theinitial climb plot with the constant 0 plot, it was seen that theinitial performance of the constant at climb is better. Because of this,the angle-of-attack indicator as a pitch control device during theinitial climb phase has an advantage.

INDICATOR DESIGN AND PERFORMANCE In the previous section on flightmechanics, it was shown that numerous flight parameters were availableto indicate the take-off performance of an aircraft. In this section,the feasibility of combining these parameters as inputs to an indicator,which can be used by the pilot to guide the aircraft during the take-offphase, is explored.

To assist in the design and evaluation of the various indicators, eachindicator was evaluated on the analog computer. From the computer,altitude-versus-distance and parameter-versus-tirne plots were recordedunder conditions of normal and reduced thrust for each indicator. Thecombination safely producing the maximum altitude in the shortestdistance under all thrust conditions was selected for further analysis.

Preliminary considerations Prior to the development of the indicator,several conditions and limitations of the analysis were determined. Theground-roll phase of take-off was not included, because in this phaseonly lateral control by the pilot is necessary. However, to minimize theground roll and initiate lift-off as soon as possible, the aircraft isrotated to :the maximum allowable angle of attack just as the lift-offvelocity is attained. For the KC aircraft, a =l2 and V =276 f.p.s. Thisairspeed and angle of attack constitute the initial condition for allindicator evaluations.

Since the critical period of take-off was established to be betweenlift-off and 500 feet, the indicator evaluation was not consideredbeyond this altitude (initial climb phase). During this period, theaircraft was considered to have had gear down and 30 flaps. In order tosimulate the loss of one engine, thrust was reduced 25% at various timesduring take-off. It was reduced at lift-ofl, lift-off plus seconds, andlift-off plus seconds. As stated earlier, asymmetric forces wereneglected for these powerloss simulations. The results of all runs werecompared for each indicator combination.

Parameter selection Although numerous flight parameters can be obtainedwith the computer, some of these parameters cannot be obtained inflight. Sensors which have the degree of accuracy, sensitivity, .andnecessary dynamics are not readily available. Consequently, aninstrument using these parameters would not be realistic. However, itwas determined that or, V, V, 9, h, and h could be obtainedsatisfactorily.

From the aircraft equations of motion, it was seen that a, 7, and/or Vcould be used to control the aircraft. However, in the indicator design,only or and V were used because of their sensor availability, fasterresponse, and direct relationship to present control systems. Therefore,in the design of the instrument, the aircrafts attitude was determinedon the analog computer by controlling a and/ or V in the equations ofmotion.

Indicator selection The approaches leading to the indicator developmentwere varied. A complete analytical approach was limited because of themany parameters and their non-linear nature. Besides the analyticalapproach, three other approaches were used. These were:

(1) An acceleration-modified approach; (2) a velocitymodified approach;and (3) a pilot technique approach.

In each of these approaches, a controlling function determined one ofthe variables in the aircrafts equations of motion Equations 1 and 2.These controlling functions were:

Each of these controlling functions was incorporated in an indicatorwhich was then analyzed on the analog computer. The performance of eachindicator was then compared against the design standards previouslymentioned. The results are shown in FIGS. 11a and 11b. It was decidedthat no single controlling function furnished satisfactory resultsthroughout the initial climb. However, by combining the constant a andthe constant ve locity controlling functions into one indicator, amaximum take-01f performance could be obtained. The following relates tothis selected indicator.

Constant angle of attack By referring to the altitude-versus-distanceplot in FIG. 11b and the time plots in FIG. 8, it can be seen that aconstant a climb produces maximum performance until V goes to zero.After this, remains positive only at the expense of V. A continuation ofconstant on results in the phngoid, as explained in the previoussection. However, if a constant a take-off is maintained until V goes tozero, then this portion of the climb phase will be maximized.

Constant velocity From Equations 1 and 2, it can be seen that a maximumclimb angle is obtained if all excess thrust is used to produce 7. Thismeans that, with V at zero, any excess thrust mus-t necessarily be usedto obtain a positive Since the constant or portion of the take-off endswith V at zero, maximum performance should continue to be obtained if Vis kept at zero. This flight condition, however, can not be allowed atlift-off. At lift-off, the lift and weight components are equal. If V isto remain constant, a sharp increase in the angle of attack would I aveto be made in order to keep V constant, to increase the lift, togenerate a positive '3 and to start climbing. Even neglecting thepossibility of the aircraft dragging its tail, as would happen with aKC-135, this situation would also lead to a difficult control problemfor the pilot, since V is much too slow for the initial climb. Anotherdisadvantage of holding V constant is that the airspeed indicator isunreliable close to the ground. The actual airspeed may be quitedifferent from an indicated airspeed because of erratic static pressuredue to airflow and ground effects. These disadvantages eliminate aconstant velocity path without a transition phase. However, if thesefaults are neglected, the results of using a constant V are shown inFIGS. 12 and 13.

Therefore, by using constant a to transition from V to the climbvelocity and to gain an initial altitude, a safe, controllable clim-bspeed can be established. The results of a constant aconsta.nt V climbare shown in FIGS. 14 and 15 on the parameter time plots andaltitude-versus-distance plots. A comparison with the other climbscleanly shows the advantages of using the selector indicator.

A take-01f indicator to direct the take-off of an aircraft in accordancewith the above constant 06-C0I1St3'11t V program is shown in logicalform in FIG. 16. A practical embodiment is shown in FIG. 17. Thetake-off is accomplished in two phases. The first phase begins with theground roll, includes lift-off and ends when the aircraft accelerationhas fallen to zero. The second phase begins ."when the first phase endsand extends to the conclusion of the takeaofif, usually considered to bewhen the aircraft has attained an altitude of 500 feet.

Referring to FIG. 16, there are four inputs to the takeoff indicator,namely, the acceleration (V) input obtained from acceleration sensor 10,the rate-of-change of pitch (6) input obtained from pitch angle sensor11, the angle of attack (04) input obtained from @angle-of-attack sensor12 and the velocity (V) input obtained from air-speed sensor 13. All ofthese sensors are standard items presently available.

The phase in which the indicator is operating and the transition fromphase 1 to phase 2 are controlled by the V sensor outiput. For thispurpose the output of this sensor is applied to switch actuator 14 whichoperates the ganged contacts of switch K downward, as seen in thedrawing, in the presence of a V output and operates the contacts upwardwhen V=0. When the aircraft is rolling down the runway, prior to itsrotation to take-off attitude, its velocity is increasing and theresulting output from the V sensor 10 causes the switch actuator 14 tooperate the switch K to its phase 1 position. During this period thereis no change from the horizontal attitude of the aircraft and,consequently, oz and 0 are both zero. In phase 1, the output of the 0sensor is applied through contact K and level adjusting device 15 tosumuning network 16 along with the outputs from the a sensor 12 and therotation programmer 17. The device 15 is a means for either decreasingor increasing the magnitude of the sensor output as required by thecharacteristics of the particular aircraft. The 9 and or outputs areapplied to summing device 16 in aiding rela-

